ISSN:
0271-2091
Keywords:
Least squares
;
Finite element
;
p-version
;
Error functional
;
Power-law-fluid
;
Non-isothermal
;
Degrees of freedom
;
p-convergence
;
Hierarchial
;
Newton's method
;
Line search
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
This paper presents a p- version least squares finite element formulation (LSFEF) for two-dimensional, incompressible, non-Newtonian fluid flow under isothermal and non-isothermal conditions. The dimensionless forms of the diffential equations describing the fluid motion and heat transfer are cast into a set of first-order differential equations using non-Newtonian stresses and heat fluxes as auxiliary variables. The velocities, pressure and temperature as well as the stresses and heat fluxes are interpolated using equal-order, C0-continuous, p-version hierarchical approximation functions. The application of least squares minimization to the set of coupled first-order non-linear partial differential equations results in finding a solution vector {δ} which makes the partial derivatives of the error functional with respect to {δ} a null vector. This is accomplished by using Newton's method with a line search.The paper presents the implementation of a power-law model for the non-Newtonian Viscosity. For the non-isothermal case the fluid properties are considered to be a function of temperature. Three numerical examples (fully developed flow between parallel plates, symmetric sudden expansion and lid-driven cavity) are presented for isothermal power-law fluid flow. The Couette shear flow problem and the 4:1 symmetric sudden expansion are used to present numerical results for non-isothermal power-law fluid flow. The numerical examples demonstrate the convergence characteristics and accuracy of the formulation.
Additional Material:
31 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650180202
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